The present invention relates to an aqueous coating composition comprising at least one aqueous dispersion comprising at least one copolymer (CP), said copolymer (CP) being preparable by (i) initially charging an aqueous dispersion of at least one polyurethane, and then (ii) polymerizing a mixture of olefinically unsaturated monomers in the presence of the polyurethane from (i), in which (a) a water-soluble initiator is used, (b) the olefinically unsaturated monomers are metered in such that a concentration of 6.0% by weight, based on the total amount of olefinically unsaturated monomers used for polymerization, in the reaction solution is not exceeded over the entire reaction time, and (c) the mixture of the olefinically unsaturated monomers comprises at least one polyolefinically unsaturated monomer and at least one linear hydroxy-functional reaction product (R) having an acid number less than 20 mg KOH/g, the preparation of which involves using at least one compound (v) containing two functional groups (v.a) and an aliphatic or araliphatic hydrocarbyl radical (v.b) which is arranged between the functional groups and has 12 to 70 carbon atoms. The present invention also relates to a method for producing a multicoat paint system using the coating composition, and to the multicoat coating thus produced.